Calculate motion ratio from shock travel and wheel travel, or estimate wheel rate from spring rate and motion ratio in metric or imperial units.

Use travel magnitudes measured over the same suspension movement.

Motion Ratio Formula

The following formula is used to calculate the Motion Ratio. 

MR = dS / dW
  • Where MR is the dimensionless Motion Ratio (shock travel / wheel travel)
  • dS is shock travel magnitude (in, mm, or cm) 
  • dW is wheel travel magnitude, expressed in the same units as shock travel 

To calculate the motion ratio, divide shock travel by wheel travel measured over the same suspension movement and in the same units. This is an average over that travel interval. For a linear spring with a locally constant spring / wheel motion ratio, wheel rate = spring rate × MR²; use the spring displacement ratio if it differs from shock travel.

How to Calculate Motion Ratio?

The following example problems outline how to calculate Motion Ratio.

Example Problem #1:

  1. First, determine the change in shock position (in).
    • The change in shock position (in) is given as 2.5.
  2. Next, determine the change in wheel position (in).
    • The change in wheel position (in) is provided as 4.
  3. Finally, calculate the Motion Ratio using the equation above: 

MR = dS / dW

The values given above are inserted into the equation below and the solution is calculated:

MR = 2.5 / 4 = .625

FAQ

What is the importance of calculating the Motion Ratio in vehicle dynamics?

The Motion Ratio is crucial in vehicle dynamics as it directly affects the vehicle’s handling and ride comfort. By understanding the Motion Ratio, engineers can design suspension systems that offer an optimal balance between comfort and handling, ensuring that the vehicle performs well under various driving conditions.

Can the Motion Ratio vary for different types of vehicles?

Yes, the Motion Ratio can vary significantly between different types of vehicles due to variations in suspension design, vehicle weight, and intended use. For example, a sports car may have a different Motion Ratio compared to a heavy-duty truck because each vehicle is designed with specific performance goals in mind.

How does changing the Motion Ratio affect a vehicle’s performance?

Using the shock / wheel convention here, a higher motion ratio increases the spring contribution to wheel stiffness when spring rate and other geometry are held constant. Motion ratio alone does not predict handling quality or identify the suspension type. The ratio may change through suspension travel; tyre stiffness and anti-roll bars also affect the vehicle.